Q. 244.1( 52 Votes )
Show that the rig
Let r and h be the radius and height of the cone respectively.
Then, the volume (V) of the cone is given by:
The surface area (S) of the cone
S = πrl
So, when then > 0
Then, by second derivative test, the surface area of the cone is the least when .
So when then h =
Therefore, for a given volume, the right circular cone of the least curved surface has an altitude equal to √2 times the radius of the base.
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